1. Field of the Invention
The present invention relates to a method for establishing a simulating signal suitable for estimating a complex exponential signal, more particularly to a method for establishing a simulating signal suitable for estimating a complex exponential signal using quadratic interpolation for correcting parameters of the simulating signal.
2. Description of the Related Art
Dynamic behavior of a physical system, such as vibration, circuit transient, etc., generally can be described by differential equations. Solutions of the differential equations generally are complex exponential functions. A parameter set of the complex exponential functions includes a frequency parameter, an amplitude parameter, a phase parameter, and a damping parameter. When the damping parameter is zero, a signal of the physical system is periodic. When the damping parameter is not zero, the signal of the physical system is not periodic, and the amplitude of the signal gradually decreases to zero with time. The physical system can be analyzed, simulated, and controlled effectively via estimation of the parameters of the simulating signal of the physical system.
However, there are a picket-fence effect and a leakage effect when transforming the time domain sampling signal of the physical system to a frequency domain signal using Fast Fourier Transform. Thus, discontinuous truncate points of a waveform in the time domain signal cause scattering of energy components in the frequency domain onto adjacent components on the frequency scale. There is thus a need to find more accurate ways of estimating dynamic behavior of physical systems.